Analysis of stirred tanks with two‐zone models

Stirred tank turbulence and fluid flow characteristics are analyzed based on a two‐zone model. Instead of using the zonal model for stirred tank performance prediction as often proposed in the literature, the zoning is used here as a tool for mixing analysis. A systematic zoning approach is proposed, where the tank is divided into two nested regions. By gradually increasing the inner zone volume, continuous curves can be obtained for turbulent energy dissipation distribution and pumping numbers between the zones as functions of the zone sizes. It is shown here that these curves can be used as a powerful tool for visualizing stirred tank performance. They can be used, e.g., in impeller performance comparisons and analysis of mixing characteristics with changing rheology, or to examine various numerical aspects related to stirred tank CFD modeling. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

液固散式流态化CFD模拟中曳力模型的影响

基于无黏性双流体简化模型在商业化软件平台上,通过增加用户自定义子程序考察了Gidaspow、Syamlal-O’Brien、Di Felice、Gibilaro、Dallavalle和BVK曳力模型对液固散式流态化CFD模拟结果的影响行为,探讨了相应的影响机制。经与文献中不同颗粒Reynolds数的代表性实验数据对比后发现：BVK和Dallavalle曳力模型对床层膨胀高度和整体固含率的预测精度较高;BVK、Syamlal-O’Brien以及Dallavalle曳力模型给出的床内固含率径向分布较为准确;BVK曳力模型较为准确地再现了颗粒轴向速度的径向分布特征。BVK曳力模型的影响机制与液固散式流态化中颗粒动力学特性相符合,在所考察范围内其预测性能最优;Dallavalle曳力模型在其余5个传统模型中预测性能较优且形式简洁在程序中易于实现。     

The influence of inclined plates on expansion behaviour of solid suspensions in a liquid fluidised bed — A computational fluid dynamics study

A significant increase in the particle sedimentation rate can be achieved by introducing inclined plates into conventional fluidised beds. In turn, high suspension densities are possible at fluidisation velocities in excess of the particle terminal velocity. The installation of the inclined plates, however, alters the dynamic characteristics of the fluidised bed, in particular, impacting upon the expansion behaviour of the suspension. In the present work a Computational Fluid Dynamics (CFD) approach was employed to investigate the influence of inclined plates on the expansion behaviour of solids suspensions in liquid fluidised beds. The model is based on the solution of the Eulerian multiphase equations for up to two different particle sizes with a continuous phase of water. The momentum equations treat hindered settling behaviour via the inclusion of a volume fraction dependent drag law. The computational model was validated against our experimental data and compared with the predictions of a kinematic model developed in one of our earlier works. In general the predictions made by both the CFD and the kinematic models were found to be in good agreement with the experimental results.     

Validation of CFD simulations of a stirred tank using particle image velocimetry data

Methods for validating CFD simulations based on the Reynolds Average Navier-Stokes equation (RANS) against Particle Image Velocimetry (PIV) measurements are investigated and applied to one of the most common problems in the chemical process industry — the prediction of flow field in a stirred vessel. A total of 1024 sequential instantaneous 2D velocity fields along the central axial plane of a stirred vessel with a P-4 axial impeller are obtained through PIV measurement. From the PIV data, the mean velocity, turbulent kinetic energy, Reynolds stresses and dissipation rate fields are extracted. By introducing several tools to quantify the similarities and differences between two-dimensional fields, CFD predictions of the flow field are validated against PIV data. Furthermore, using PIV and LDV data, the effect of boundary conditions on CFD simulation results is examined. The effect of different Reynolds stress closures on the flow prediction is also studied.     

侧进式搅拌釜内气液两相流的数值模拟

采用计算流体力学(CFD)技术对φ1.5 m×1.2 m侧进式气液搅拌釜内气液两相流场进行数值模拟,检验了3种气液分界面边界条件和两种相间曳力模型。通过UDF程序将上述模型分别与欧拉双流体模型和 dispersed k-ε 两相湍流模型进行耦合计算,得到搅拌功率准数、总体气含率和气相分布,并与冷模实验结果进行对比,得到能准确预测的CFD模型。研究结果表明,3种气液界面边界条件下采用标准S-N模型计算所得的功率准数和气体分布误差均较大,而Brucato-Tsuchiya模型的预测结果更接近实验结果;气液界面边界条件对总体气含率的预测影响较大,采用速度进口或脱气边界和Brucato-Tsuchiya模型耦合计算所得的结果误差比压力出口边界明显要小。     

CFD simulation of stirred tanks: Comparison of turbulence models. Part I: Radial flow impellers

A critical review of the published literature regarding the computational fluid dynamics (CFD) modelling of single‐phase turbulent flow in stirred tank reactors is presented. In this part of review, CFD simulations of radial flow impellers (mainly disc turbine (DT)) in a fully baffled vessel operating in a turbulent regime have been presented. Simulated results obtained with different impeller modelling approaches (impeller boundary condition, multiple reference frame, computational snap shot and the sliding mesh approaches) and different turbulence models (standard k ? ε model, RNG k ? ε model, the Reynolds stress model (RSM) and large eddy simulation) have been compared with the in‐house laser Doppler anemometry (LDA) experimental data. In addition, recently proposed modifications to the standard k ? ε models were also evaluated. The model predictions (of all the mean velocities, turbulent kinetic energy and its dissipation rate) have been compared with the experimental measurements at various locations in the tank. A discussion is presented to highlight strengths and weaknesses of currently used CFD models. A preliminary analysis of sensitivity of modelling assumptions in the k ? ε models and RSM has been carried out using LES database. The quantitative comparison of exact and modelled turbulence production, transport and dissipation terms has highlighted the reasons behind the partial success of various modifications of standard k ? ε model as well as RSM. The volume integral of predicted energy dissipation rate is compared with the energy input rate. Based on these results, suggestions have been made for the future work in this area.     

Hysteresis in cloud heights during solid suspension in stirred tank reactor: Experiments and CFD simulations

Solid suspension in stirred tank reactor is widely used in process industries for catalytic reactions, dissolution of solids, crystallization, and so on. Suspension quality is a key issue in design and operation of stirred reactor and its determination is not straight forward. Cloud height measurements of solid suspension provide a relatively simple way to quantify quality of suspension. In this work, experiments were carried out to quantify variation of cloud heights with impeller speed and particle characteristics. These measurements were carried out using visual observations, image analysis, and ultrasound velocity profiler techniques. The obtained data demonstrated the existence of hysteresis in cloud heights with respect to impeller speed. Apart from possible applications in reducing power required for achieving desired solid suspension quality, the existence of hysteresis also provides a new way to evaluate computational fluid dynamics (CFD) simulations of solid–liquid flows in stirred vessels. An attempt was made to capture observed hysteresis in cloud heights in CFD simulations. The simulated results were compared with the experimental data. The presented models and results (experimental and computational) will be useful for simulating complex solid–liquid flows in stirred reactors. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

Optimisation of vertical axis wind turbine: CFD simulations and experimental measurements

A system for the conversion of kinetic energy of wind into thermal energy has been developed which can replace relatively expensive electro‐mechanical equipment. The system consists of a vertical axis wind turbine (VAWT) which is coupled with the shaft of a stirred vessel. In the present work, computational fluid dynamic (CFD) simulations have been performed for the flow generated in a stirred tank with disc turbine (DT). The predicted values of the mean axial, radial and tangential velocities along with the turbulent kinetic energy have been compared with those measured by laser Doppler anemometry (LDA). Good agreement was found between the CFD simulations and experimental results. Such a validated model was employed for the optimisation of drag‐based VAWT. An attempt has been made to increase the efficiency of turbine by optimising the shape and the number of blades. For this purpose, the combination of CFD and experiments has been used. The flows generated in a stirred tank and that generated by a wind turbine were simulated using commercial CFD software Fluent 6.2. A comparison has been made between the different configurations of wind turbines. Results show that a provision in blade twist enhances the efficiency of wind turbine. Also, a wind turbine with two blades has higher efficiency than the turbine with three blades. Based on the detailed CFD simulations, it is proposed that two bladed turbine with 30° twist shows maximum efficiency. © 2011 Canadian Society for Chemical Engineering     

Heat transfer to liquids and suspensions in agitated narrow vessels

The knowledge of the heat transfer coefficient on the inner side of a heated vessel wall is of the utmost importance for the design of agitated vessels. In the case of large Reynolds numbers, the heat transfer is mainly determined by these numbers whereas, with small Reynolds numbers, the heat transfer is better described by considering the Grashof number. Investigations of heat transfer in agitated narrow vessels have shown that the height/diameter ratio exerts virtually no influence on the heat transfer when multi-impeller stirrers are used. The heat transfer to stirred suspensions can be described by relationships valid for liquids if the characteristic data of the liquid are replaced by those of the suspension and when the solids volume concentration is also taken into account. This relationship allows the heat transfer coefficient to be calculated for given solids volume concentrations of up to 60%.     

CFD study of solids concentration in a fluidised-bed coater with variation of atomisation air pressure

The solids volume fraction inside a tapered fluidised bed coater was simulated with the use of an Eulerian computational fluid dynamics (CFD) model with atomisation nozzle sub-model. The drag force, describing momentum transfer between the gas and solid phases was calculated using the drag model proposed by [1]. In order to account for the particle size distribution of the fluidised solid materials, a 4-phase Eulerian model was used. The model-predicted results for different atomisation air pressures were verified using published experimental data [2]. It was shown that the model proved to be highly sensitive to changes in the fluidisation air flow rate with regard to the model-predicted solids volume distribution.     

Comparison and evaluation of interphase momentum exchange models for simulation of the solids volume fraction in tapered fluidised beds

An Eulerian computational fluid dynamics (CFD) model with granular flow extension was used to simulate a gas–solid fluidised bed in a tapered reactor. Various drag coefficient models were evaluated, which are used to calculate the drag force, describing the momentum transfer between the gas and solid phases. Comparison and evaluation between time-averaged solids volume fractions obtained from experiments and from simulations with several drag coefficient models were made. The predicted results obtained by the different drag models were verified using experimental data of Depypere et al. (2009). Initial results using a 2-phase Eulerian model showed poor agreement with experimental results. However, extending the Eulerian model to include 3 solid phases—with different mean particle diameter per phase in order to account for the particle size distribution of the fluidised solid material—yielded good agreement with experimental results. Furthermore, quantitative analyses showed that the modified Gidaspow drag model gave the best agreement between CFD simulations and experimental data.     

基于EMMS模型的搅拌釜内气液两相流数值模拟

采用欧拉-欧拉模型对搅拌釜内气液两相流进行了三维CFD模拟,重点研究了采用不同曳力模型时CFD模拟对搅拌桨附近排出流区两相流动的预测能力。模拟结果表明CFD能准确地预测排出流区的液相速度分布,但采用传统的Schiller-Naumann曳力一定程度上低估了排出流区的气液相间曳力,导致在完全扩散区CFD预测的分布器和桨叶下方区域气含率偏小,而基于气液非均匀结构和能量最小多尺度（EMMS）方法得到的DBS-Global曳力模型能更准确地描述完全扩散区气液搅拌釜内流动情况。与传统曳力模型相比,采用DBS-Global曳力模型能显著提高对气含率的预测。     

CFD simulation of liquid-phase mixing in solid-liquid stirred reactor

A comprehensive CFD model was developed to gain an insight into solid suspension and its implications on the liquid-phase mixing process in a solid-liquid stirred reactor. The turbulent solid-liquid flow in a stirred reactor was simulated using a two-fluid model with the standard k-ε turbulence model with mixture properties. The multiple reference frames (MRFs) approach was used to simulate impeller rotation in a fully baffled reactor. The computational model with necessary sub-models was mapped on to a commercial solver FLUENT 6.2 (of Fluent Inc., USA). The predicted solid concentration distribution was compared with the experimental data of Yamazaki et al. [1986. Concentration profiles of solids suspended in a stirred tank. Powder Technology 48, 205-216]. The computational model was then further extended to simulate and understand the implications of the suspension quality on liquid-phase mixing process. The computational model and the predicted results discussed here will be useful for understanding the liquid-phase mixing process in stirred slurry reactors in various stages of solid suspension.     

Particle‐resolved PIV experiments of solid‐liquid mixing in a turbulent stirred tank

Particle Image Velocimetry (PIV) experiments on turbulent solid‐liquid stirred tank flow with careful refractive index matching of the two phases have been performed. The spatial resolution of the PIV data is finer than the size of the spherical, uniformly sized solid particles, thereby providing insight in the flow around individual particles. The impeller is a down‐pumping pitch‐blade turbine. The impeller‐based Reynolds number has been fixed to Re = 10⁴. Overall solids volume fractions up to 8% have been investigated. The PIV experiments are impeller‐angle resolved, that is, conditioned on the angular position of the impeller. The two‐phase systems are in partially suspended states with an inhomogeneous distribution of solids: high solids loadings near the bottom and near the outer walls of the tank, much less solids in the bulk of the tank. The liquid velocity fields show very strong phase coupling effects with the particles increasingly attenuating the overall circulation patterns as well as the liquid velocity fluctuation levels when the solids volume fraction is increased. © 2017 American Institute of Chemical Engineers AIChE J, 63: 389–402, 2018     

Calculation of the particle size distribution in suspension polymerization using a compartment-mixing model

A modelling strategy for effective estimation of the particle size distribution (PSD) in suspension polymerization is presented. The strategy consists of coupling a population balance equation (PBE) and a compartment-mixing (CM) model to account for the non-homogeneous mixing in the tank reactor. The values for the rate of energy dissipation of each compartment are estimated from Computational Fluid Dynamics (CFD) calculations and experimental reports on systems with the same agitator and geometric characteristics. Model predictions using the CM model are compared with predictions that assume homogeneous mixing and experimental data on PSD from styrene and divinylbenzene pilot-plant suspension polymerization reactors of 1 and 5 L with Rushton and PBT impellers.     

Experimental determination and numerical simulation of mixing time in a gas-liquid stirred tank

In this work, mixing experiments and numerical simulations of flow and macro-mixing were carried out in a 0.24 m i.d. gas-liquid stirred tank agitated by a Rushton turbine. The conductivity technique was used to measure the mixing time. A two-phase CFD (computational fluid dynamics) model was developed to calculate the flow field, k and ε distributions and holdup. Comparison between the predictions and the reported experimental data [Lu, W.M., Ju, S.J., 1987. Local gas holdup, mean liquid velocity and turbulence in an aerated stirred tank using hot-film anemometry. Chemical Engineering Journal 35 (1), 9-17] of flow field and holdup at same conditions were investigated and good agreements have been got. As the complexity of gas-liquid systems, there was still no report on the prediction of mixing time through CFD models in a gas-liquid stirred tank. In this paper, the two-phase CFD model was extended for the prediction of the mixing time in the gas-liquid stirred tank for the first time. The effects of operating parameters such as impeller speed, gas flow rate and feed position on the mixing time were compared. Good agreements between the simulations and experimental values of the mixing time have also been achieved.     

Modeling of the 3D hydrodynamics of 2-blade impellers in stirred tanks filled with a highly viscous fluid

This paper deals with mixing in stirred tank reactors by paddle agitators and two-blade impellers with different blade widths. Computational Fluid Dynamics (CFD) is used to solve the 3D hydrodynamics and to obtain at every point the flow patterns, the stress components and the viscous dissipation function. From the latter information, the power consumption is calculated. These results are compared with available experimental data: good agreement is observed. For example, for a paddle agitator, the flow is essentially plane far away from the horizontal walls. That means that, in order to create an axial circulation in the volume of the tank, the impeller height has to be decreased. This work documents the ability of CFD to model changes in flow patterns for three dimensional flows in stirred tanks.     

Modifying the inter‐phase drag via solid volume fraction gradient for CFD simulation of fast fluidized beds

The conventional drag model in two‐fluid simulation, which assumes uniform particle distribution in a computational grid, overestimates the drag force, thus failed in capturing the subgrid‐scale strands and resolvable‐scale clusters. This work proposed a new modification to the conventional drag model through considering the heterogeneous distribution of solid volume fraction (SVF), especially, in the inter‐phase boundary (i.e., cluster boundary). The resulting drag model is a function of particle Reynolds number, SVF and the gradient of SVF. This straightforward modification is consistent with the elaborately filtered‐approach‐based modification method in nature. A CFD simulation for a two‐dimensional riser was conducted to validate the new drag model. The outlet solid mass flux, axial and radial time‐averaged voidages from the new drag model agreed well with the experimental measurements, and these results were far better than those from the conventional homogeneous drag models. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2588–2598, 2017     

利用声发射技术测量搅拌釜的淤浆悬浮高度

根据颗粒运动碰撞搅拌釜壁面产生声波的机理,结合声信号的频谱分析、小波分解和R/S分析,获得了代表颗粒运动的特征信号频段（d1、d2频段）。同时,基于声波特征信号频段能量沿搅拌釜轴向的规律性变化,提出了声波法测量搅拌釜淤浆悬浮高度的判据,即当声波特征信号频段能量或声波特征信号频段能量比出现阶跃性变化时的高度为淤浆悬浮高度。以水-玻璃珠体系为例,研究发现,无论是盘式涡轮还是桨式叶轮的搅拌桨,基于声信号测定淤浆悬浮高度的判据都能较好地得到验证,与目测法相比,其平均相对误差小于10 %,具有较高的精度。由此,获得了一种简单快捷、灵敏准确、非侵入式的搅拌釜淤浆悬浮高度测量技术,能够实现淤浆悬浮高度的实时监控。     

改进型INTER-MIG搅拌槽内固液悬浮特性的数值模拟

应用CFD软件Fluent 12.0和并行计算机工作站对双层改进型INTER-MIG桨式搅拌槽内的固液悬浮特性、临界离底悬浮转速及功率消耗进行数值模拟,分析了在固体体积分数as=30%下,转速n、桨叶离底距离C1和桨间距C2等因素对搅拌槽内颗粒悬浮特性的影响. 结果表明,在一定的转速和桨径下,改变C1和C2会改变流场的局部结构,选取适合的C1和C2可使固液混合更均匀,有利于颗粒悬浮和整个搅拌槽传质传热的进行. 最佳桨叶离底高度与槽径比为0.36,最佳桨叶间距与槽径比为0.44;在该最佳工况下临界离底悬浮转速Njs=118.3 r/min;得到既能达到完全离底悬浮、又能使搅拌功耗最小的最佳转速为n=124 r/min.